Well, it depends on where you look. There are many fanfiction hubs out there. However, the availability of 'kiss him not me kae x mutsumi fanfiction' can vary. Some sites might have a large collection while others may have only a few. You can also try reaching out to fellow fans of the series who might be able to point you in the right direction.
Yes, there are some. You can start by checking fanfiction websites like Archive of Our Own. There might be various stories exploring the relationship between Kae and Mutsumi in the 'kiss him not me' universe.
Chapter 524, "He Faces Imprisonment", is the clearest early answer because it turns Sister Li's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Hello everyone, I'm the new director of 'Wilderness Survival 30...
Chapter 584, "The Wealthy Young Master Renounces Worldly Life for Love", is the clearest early answer because it turns Bai Lu's situation into a concrete plot event. The chapter gives readers a real answer by opening on There wasn't a mirror on the small boat.
Chapter 660, "Includes Meals and Accommodation?", is the clearest early answer because it turns Mu Ye's situation into a concrete plot event. The chapter gives readers a real answer by opening on My point exactly," Jiang Li said, "I'll pay off the over twelve...
Chapter 548, "A Guy Named Gu Yu", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. A useful checkpoint is the way the scene starts with No, we can't," Su Yinwan blurted out subconsciously.
Chapter 518, "Calculator: 438", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. The chapter gives readers a real answer by opening on I won't eliminate you." Jiang Li's statement came as a shock.
Chapter 715, "Childhood Shadow", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. The chapter turns that into something concrete by moving from Jiang Mingyu let out a long sigh before collapsing onto the sofa,...
Chapter 355, "She is My Only Sister", is the clearest early answer because it turns Mystical Skills's situation into a concrete plot event. Early on, Luo must have checked lots of news about me these past few days, so....
Chapter 349, "Everyone Who Went Out to Dinner that Night Got Poisoned!", is the clearest early answer because it turns Director Zhang's situation into a concrete plot event. The chapter turns that into something concrete by moving from The news quickly reached Ye Chu.
Chapter 368, "You Don't Deserve to Be My Mother", is the clearest early answer because it turns Du Qinglian's situation into a concrete plot event. The chapter gives readers a real answer by opening on I haven't detained anyone, how could I possibly detain him?